Example 7 - Income of a person is Rs 3,00,000 in first year - Arithmetic Progression (AP): Statement

  1. Chapter 9 Class 11 Sequences and Series
  2. Serial order wise
Ask Download

Transcript

Example 7 The income of a person is Rs. 3,00,000, in the first year and he receives an increase of Rs.10,000 to his income per year for the next 19 years. Find the total amount, he received in 20 years. Income of the person in 1st year = Rs 3,00,000 Income of the person in 2nd year = Rs 3,00,000 + 10,000 = Rs 3,10,000 Income of the person in 3rd year = Rs 3,10,000 + 10,000 = Rs 3,20,000 Thus, Income received every year is 300000, 310000, 320000,… This is an A.P as difference between consecutive terms is constant. 300000, 310000, 320000,… Here first term = a = 300000 common difference = d = 310000 – 300000 = 10000 To find the total amount received in 20 years, we use the formula Sn = n/2 ( 2a + (n – 1)d ) Where, Sn = sum of n terms of A.P. n = number of terms a = first term and d = common difference Here, Sn = Amount received in 20 years, n = 20 , a = 300000, d = 10000 Putting the values S20= 20/2 [2 × 300000 + (20 – 1)10000] S20= 20/2 [2 × 300000 + (20 – 1)10000] = 10 [ 600000 + 19 × 10000] = 10 [600000 + 190000] = 10 (790000) = 79,00,000 Thus , the total amount received at the end of 20 years is Rs. 79,00,000.

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
Jail